To evaluate the algebraic expression [tex]\(c^2 + 2cd + dz\)[/tex], we need to follow these steps:
1. Identify the Values of Variables:
Let's assume the values provided for the variables are:
- [tex]\(c = 1\)[/tex]
- [tex]\(d = 1\)[/tex]
- [tex]\(z = 1\)[/tex]
2. Calculate Each Term Individually:
- First Term: [tex]\(c^2\)[/tex]
[tex]\[
c^2 = 1^2 = 1
\][/tex]
- Second Term: [tex]\(2cd\)[/tex]
[tex]\[
2 \cdot c \cdot d = 2 \cdot 1 \cdot 1 = 2
\][/tex]
- Third Term: [tex]\(dz\)[/tex]
[tex]\[
d \cdot z = 1 \cdot 1 = 1
\][/tex]
3. Add the Results of Each Term Together:
Now, sum all the terms:
[tex]\[
c^2 + 2cd + dz = 1 + 2 + 1
\][/tex]
4. Compute the Final Result:
Adding these values together:
[tex]\[
1 + 2 + 1 = 4
\][/tex]
Therefore, the value of the expression [tex]\(c^2 + 2cd + dz\)[/tex] when [tex]\(c = 1\)[/tex], [tex]\(d = 1\)[/tex], and [tex]\(z = 1\)[/tex] is:
[tex]\[
\boxed{4}
\][/tex]
Additionally, the individual terms are:
- [tex]\(c^2 = 1\)[/tex]
- [tex]\(2cd = 2\)[/tex]
- [tex]\(dz = 1\)[/tex]
Thus, the complete results are:
[tex]\[
(1, 2, 1, 4)
\][/tex]
